Single-particle correlations in events with the total disintegration of ...

Single - particle correlations in events with the total disintegration of nuclei

M. K. Suleimanov [] , O. B. Abdinov and A. M.Bagirov

arXiv:hep-ex/9712025v1 18 Dec 1997

Physics Institute, Azerbaijan Academy of Sciences, Baku, Azerbaijan Republic

A.I.Anoshin Nuclear Physics Institute, Moscow State University, Moscow, Russia

J.Bogdanowicz Soltan Institute for Nuclear Studies, Warzaw, Poland and Joint Institute for Nuclear Research, Dubna,Russia

A.A.Kuznetsov Joint Institute for Nuclear Research, Dubna,Russia

∗

Now at the Laboratory of High Energies, JINR, 141980 Dubna, Russia . Electronic address:[email protected]

1

New experimental data on the behaviour of the single - particle two-dimensional correlation functions R versus Q (Q is the number of nucleons emitted from nuclei) and Ap (Ap is the mass of projectile nuclei) are presented in this paper . The interactions of protons, d, 4 He and

12

C nuclei

with carbon nuclei ( at a momentum of 4.2 A GeV/c) are considered. The values of R are obtained separately for π − mesons and protons. In so doing, the values of R are normalized so that −1 ≤ R ≤ 1. The value of R = 0 corresponds to the case of the absence of correlations. It has been found that the Q- and Ap -dependence of R takes place only for weak correlations (R < 0.3). In the main (90 %),these correlations are connected with the variable pt and have a nonlinear character, that is the regions with different characters of the Q-dependence of R are separated: there is a change of regimes in the Q-dependences of R. The correlations weaken with increasing Ap , and the variable R gets the least values of all the considered ones in

12

CC interactions. Simultaneously

with weakening the correlations in the region of large Q , the character of the Q-dependence of R changes. The work has been performed at the Laboratory of High Energies, JINR. PACS number(s): 25.70.Np, 25.45.-z, 22.55.-e

I. INTRODUCTION The aim of this paper is to give information on the values of single-particle correlation functions (R) in nucleus-nucleus collisions and in events with TDN . The study of correlation effects in particle production is the source of information on the dynamics of interactions supplementing the information obtained from the single-particle inclusive distributions, from the analysis of the mean characteristics and so on. [1].

2

In this paper, we present the results of investigating the Q-dependence

∗

of R for π − mesons and

protons emitted in nucleus-nucleus collisions. Such an experiment allows us to obtain necessary information. Interest in the processes of TDN is determined by that they are extreme cases. It is supposed that in these cases the anomalously large densities of nuclear matter can be realized, and the effects associated with the collective properties of nuclear matter are revealed. We think that the processes of TDN correspond to qualitatively new states of nuclear matter, and the transition to these states goes through the ”critical” values of Q → Q∗ . The presence of Q∗ should lead to changing in the Q dependences of event characteristics in the region near - Q∗ . Therefore, it is offered to use the condition Q ≥ Q∗ as an event selection criterion with the total disintegration of target nuclei. The probability distributions of observing pC, dC, 4 HeC and

12

CC events with the given values

of the variable Q are studied in papers [2]. The dependences of the mean characteristics and the inclusive spectra of secondary π mesons and protons on Q are studied in papers [3-4] † . The results , obtained in these papers , confirm our assumption that a critical value of Q∗ for Q exists (its excess leads to the TDN ) . The single-particle two-dimensional correlation function R( x, z ) is used in the analysis. It is connected with that the correlations strengthen when passing to high orders of R [5-7]. The values of R( x, z ) for the variables x, z were calculated by the following formula: R(x, z) = (Exz − ExEz)/(σ(x)σ(z))

∗

The values of Q were determined as Q is Q = N+ − Nπ− ( N+ and Nπ− are the numbers of positive

charged particles and π − mesons , respectively ) .The variable Q is proportional to the number of protons emitted from nuclei during the interaction. In detail, using the variable Q ,see paper [2] . † For this, the groups of events with Q ≥ 1; 2; 3; ... were defined. Then, the mean characteristics and the invariant inclusive spectra were obtained for each group.

3

Here Exz is the mixed mathematical expectation of quantities x and z ; Ex and Ez are the mathematical expectations of x and z, respectively ; σ(x) and σ(z) are the r.m.s. deviations of x and z , respectively. To evaluate Exz, Ex, Ez, σ(x) and σ(z), the following formulae were used : Exz = (1/N)

P40 P40 i=1

j=1

Ex = (1/N)

P40

Ez = (1/N)

P40

i=1

Nij xi zj

Ni xi

j=1 Nj zj

σ(x) = (Ex2 − (Ex)2 )1/2 , σ(z) = (Ez 2 − (Ez)2 )1/2 Ex2 = (1/N)

P40

i=1

Ni x2i , Ez 2 = (1/N)

P40

j=1

Nj zj2

In these formulae , Nij is the number of particles hitting an (i, j) -th cell . N=

P40 P40 i=1

j=1

Nij , Ni =

P40

j=1 Nij ,

Nj =

P40

i=1

Nij

During the construction of the two-dimensional distributions for the chosen variables , the intervals , corresponding to them were divided into 40 subintervals.

II. METHODS OF THE EXPERIMENT

The experimental data have been obtained from the 2-m propane bubble chamber of LHE, JINR . The chamber placed in a magnetic field of 1.5 T, was exposed to beams of light relativistic nuclei at the Dubna Synchrophasotron. Practically all secondaries emitted at a 4π total solid angle were detected in the chamber. All negative particles, except identified electrons, were considered as π − mesons. The contaminations by misidentified electrons and negative strange particles do not exceed 5% and 1%, respectively.The average minimum momentum for pion registration is about 70 Mev/c. The protons were selected by the statistical method applied to all positive particles with a momentum of p >500 MeV/c ( we identified slow protons with p ≤700 Mev/c by ionization in the chamber). In this experiment, we used 5284 pC , 6735 dC , 4852 4 HeC and 7327 4

12

CC interactions

at a momentum of 4.2 A GeV/c ( for methodical details see [9]) . The available statistical material was separated into groups of events with the following values of Q: Q ≥ 1; 2; 3; ..Q∗; ... (1) The values of R were determined for π − mesons and protons from these groups of events. In this case , we considered only π − mesons and protons with the errors in measuring the momenta not exceeding 30 %. We considered the following correlation functions R( p, θ ), R( p, pt ) , R( p, y ) , R( p, β ), R( θ, pt ) , R( θ, y ), R( θ, β 0 ), R( pt , y ) ,R( pt , β 0 ) ,R( y, β 0 ) , where : - p are momenta in the laboratory coordinate system (lcs) - θ - emitted angles in the lcs - pt - transverse momenta, - y - rapidities in the lcs. β 0 - orders of cumulativity ( here β 0 = (E-pL ) / mN , E is the total energy (in the lcs), pL is the longitudinal momentum (in the lcs) and mN is the nucleon mass ). The correlations between pt and pL for π − mesons , produced in dC interactions at 1.7 and 4.2 GeV/c per nucleon , were studied in paper [10]. The dependence of the distribution density π − mesons on these variables was observed. The forms of these distributions turned out to depend on beam energy. The y and pt distributions of protons were measured in S+W, O+W and p+W reactions at 200 GeV/A [11]. The density of the y distribution was found to grow linearly with increasing transverse energy for all the 3 reactions . However, the slope in p+W is sharper than in O +W and S+W. The rapidity density in p+W is much larger than it was predicted on the basis of summing nucleus-nucleus collisions without taking into account nuclear effects pointing to the importance of rescattering effects. The results obtained in papers [10 - 11] show a good perspective of using the R function for revealing qualitatively new phenomena in interactions of relativistic nuclei. In our experiment , the parameters β 0 , θ, y were chosen in the intervals : 0 ≤ β 0 ≤ 3; 0 ≤ θ ≤ 1800 and −2 ≤ y ≤ 3.5 in all cases. 5

The parameters p and pt in pC, dC, 4HeC, 12CC interactions were chosen from the intervals : 0.07GeV /c ≤ p ≤ 10GeV /c and 0.07GeV /c ≤ pt ≤ 4GeV /c both for protons and for π − mesons.

III. THE RESULTS OF THE EXPERIMENT AND DISCUSSION

The values of R at different Q for different pairs were obtained using the method described above. In all , the Q-dependences for 100 R functions were obtained ( 10 types of R functions separately for π − mesons and protons in 5 types of interactions, see above). According to the character of the Q - dependence of R , the data can be divided into two groups : group I - the data on the Q independence of R and group II - the data showing the Q dependence of R . The data from the first group were fitted with an a ∗ Q + b expression , where a ( for this group of data , the values of a turned out to be close to

6

zero.) and b are the fitting parameters ‡ . The values of b are presented in tables I and II. The cases from the second group are denoted by dashes. The absolute values of R depending on Q for this group of data are shown in figures 1-5 ( the curves are hand-drawn ) § . From the data in tables I-II, one can see the following: - the Q-dependence of R is not observed in 71 % cases (of 100, group I of data), and the function R respectively depends on Q (group II of data) in 29 % cases , - in 90 % cases of group II the Q-dependence of R is mainly due to the variable pt , - the data from group I also point to the independence of the behaviour of projectile mass (Ap ) in nucleus-nucleus interactions. From figs. 1-5, one can draw the following conclusions : - in 75 % cases , the Q-dependence of R has a nonlinear character , i.e. the regions with different Q-dependences of R are separated or the change of regimes takes place in these dependences. The totality of these data allows one to determine the ” critical” values of Q = Q∗ corresponding to the transition from one region to another. These values of Q∗ mainly coincide with those obtained in previous papers [1-3] and are used for event selection with TDN. Thus , we have that the correlation analysis also confirms that events with TDN qualitatively differ from ”usual” events, and it is necessary to use condition (1) for their separation. This confirms our main affirmation that the TDN processes are those in which so a large (”critical” ) fraction of nuclear nucleons is emitted whose excess leads to showing qualitatively new properties (see paper [1]). In particular , from the

‡ §

We do not present the measured errors of b but take them into account in our conclusions. We do not present the data on a) the values of R(p, β 0 ) depending on Q in pC interactions (for

π − mesons and protons) and dC interactions (for protons). For these cases , the values of R(p, β 0 ) decrease with increasing Q. In so doing , this dependence has a linear character for π − mesons and almost a logarithmic character for protons ; b) the values of R(pt , β 0) as in this case the behaviour of R versus Q for pC , dC and 4 HeC interactions is similar to those shown in figs. 3-5. For

12

CC

interactions , the behaviour of R(pt , β 0 ) as a function of Q is a line with ”break” in its character.

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analysis results presented in the above figures , it has been found that - 82 % of cases from group II have R < 0.3, i.e. weak correlations related to the variable pt and depending on Q , mainly take place ; - in all the considered cases , a strong change of the form of the Q- and A − p-dependences of | R | is observed. For example , the correlations weaken with increasing Ap , and the variable R gets the least values of all the considered ones in 12 CC interactions ( this result agrees well with the conclusions of paper [11]). The character of the Q - dependence of | R | also changes simultaneously with weakening the correlations in the region of large Q ( TDN region ) This dependence is a line with ”break” for pC , dC interactions , it is of the step-by step form for 4 HeC interactions and the ”zigzag” form for

12

CC interactions. It is possible that the ”zigzag” form is the result of the

influence of density fluctuations of nuclear matter in the TDN region on these dependences . In earlier paper [12] (in the studies of the multiplicity distributions and their second moments for negative charged particles produced in ”central” collisions (”central”) and in interactions of minimum trigger in

32

S + S collisions at 200 A GeV over different rapidity intervals ), it has been found that the

models of FRITIOF and VENUS mainly describe the dependence of second moments on rapidity intervals for the events with minimium trigger and not for ”central”. The conclusion has been drawn that the behaviour of second moments for ”central” indicates increasing the multiplicity fluctuation . These observations support the conclusions from the analysis of entropy. The entropy for central 32

S + S is larger than that expected in the models. The results of the present paper also confirm this

conclusion. We also think that the ”zigzag” form in events with the total disintegration of nuclei can be connected with the density fluctuations of nuclear matter at large Q. Under these experimental conditions , we observed a strong Q-dependence of the mean values of the kinetic energy of π − mesons in

12

CC interactions in the region Q ≥ Q∗ - of the total disintegration

of nuclei. The present results show that this is possibly due to the fluctuations of nuclear density in events with the total disintegration of nuclei. It has already been concluded [13] that the transparency of nuclear matter in ”central” decreases significantly. In the authors’ opinion , it testifies of a high baryon density reached in the investigated interactions. We assume that at our energies they are mixed states corresponding to different degrees of freedom , as well as quark - gluon degrees of

8

freedom; - for protons, the behaviours of R(θ, pt ) (fig. 4) and R(pt , y) (fig. 5) versus Q are similar and differ from the behaviour of the Q - dependence of R(p, pt ) ( fig. 3).

ACKNOWLEDGEMENTS

The authors consider it their pleasant debt to thank the staff of the 2-m propane bubble chamber for giving the experimental material, N. Amelin and A. Golokhvastov for useful discussions , O. Rogochevsky for his help and also Academician A. M. Baldin for his permanent attention to work.

[ 1 ] E. A. De Wolf , I. M. Dremin , W. Kittel . Russian Journal UFN , 163 , 3 , (1993) [ 2 ] O. B. Abdinov. et al. , JINR Rapid Communications No. 1[75] , 51 , (1996) . [ 3 ] O. B. Abdinov et al. , JINR Rapid Communications No. 1[81] ,109 , (1997) . [ 4 ] O. B. Abdinov et al. , JINR Communications No. E1-97-178 , 1, (1997) . [ 5 ] P. Abreu et al. , Phys. Lett. B247 , 137 , (1990) ; A. De Angelis Mod. Phys. Lett. A5 , 2395 , (1990). [ 6 ] I. V. Ajienko et al. , Phys. Lett. B222 , 306 , (1989) ; I. V. Ajienko et al. , Phys. Lett. B235 , 373 , (1990) ; N. M. Agababyan et al. , Phys. Lett. B261 , 165 , (1991). [ 7 ] C. Albajar et al. , Nucl. Phys. B345 , 1 , (1990). [ 8 ] The BBCDHSSTTU-BW Collaboration , A. U. Abdurakhimov et al. , Phys. Lett. , B39 , 371 , (1972). 9

[ 9 ] N. Akhababian et al. , JINR Preprint 1-12114 , (1979). [ 10 ] K. N. Ermakov , O. V. Rogochevskiy , M. V. Stabnikov , Preprint RAS , 2012 , 1 ,(1994). [ 11 ] T. Akesson et al. , Z. Phys. C. 53 , 183 , (1992). [ 12 ] J. Bachler et al. , Z. Phys. C. , 56 , 347 , (1992) [ 13 ] J. Berrette et al. , Phys.Rev. C. 50 , 3047 , (1994).

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FIG. 1. Q-dependence of | R(θ, pt ) | for π − mesons in pC , dC ,4 HeC and

12

CC interactions. The values of R shown at

Q = 1; 2; 3; ... correspond to the groups of events with Q ≥ 1; 2; 3; ... , respectively.

FIG. 2.

Q-dependence of | R(pt , y) | for π − mesons in pC , dC ,4 HeC and

12

CC interactions. The values of R shown at

Q = 1; 2; 3; ... correspond to the groups of events with Q ≥ 1; 2; 3; ... , respectively.

FIG. 3. Q-dependence of | R(p, pt ) | for protons in pC , dC ,4 HeC and

12

CC interactions. The values of R shown at

Q = 1; 2; 3; ... correspond to the groups of events with Q ≥ 1; 2; 3; ... , respectively.

FIG. 4. Q-dependence of | R(θ, pt ) | for protons in pC , dC ,4 HeC and

12

CC interactions. The values of R shown at

Q = 1; 2; 3; ... correspond to the groups of events with Q ≥ 1; 2; 3; ... , respectively.

FIG. 5. Q-dependence of | R(pt , y) | for protons in pC , dC ,4 HeC and

12

CC interactions. The values of R shown at

Q = 1; 2; 3; ... correspond to the groups of events with Q ≥ 1; 2; 3; ... , respectively.

11

TABLE I. For π − mesons

Type

pC

dC

4

HeC

12

CC

of events. R(p, θ) - 0.49 - 0.52 - 0.49 - 0.48 R(p, pt )

0.62 0.52 0.49 0.50

R(p, y)

0.67 0.71 0.70 0.69

R(p, β 0)

-

-

R(θ, pt )

-

-

R(θ, y)

-0.22 -0.19 -

-

-0.93 -0.92 -0.91 -0.90

R(θ, β 0 ) 0.83 0.78 0.79 0.78 R(pt , y)

-

-

-

-

R(pt , β 0 ) 0.31 0.42 0.43 0.45 R(y, β 0) -0.79 -0.73 -0.73 -0.71

TABLE II. For protons

12

Type

pC

dC

4

HeC 12 CC

of events R(p, θ) -0.67 -0.68 -0.63 -0.63 R(p, pt )

-

-

-

-

R(p, y) 0.97 0.96 0.93 0.93 R(p, β 0 )

-

R(θ, pt )

-

-0.85 -0.80 -0.78 -

-

-

R(θ, y) -0.80 -0.81 -0.80 -0.82 R(θ, β 0 ) 0.90 0.90 0.92 0.93 R(pt , y)

-

-

-

-

R(pt , β 0 )

-

-

-

-

R(y, β 0) -0.94 -0.95 -0.94 -0.94

13